Question 1

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Partial excel results are summarized below:  Given this information alone, would you decide to continue with the regression analysis?
A) Yes, because the information is based on a significant size sample.
B) Yes, because the multiple r value is large
C) No, because the multiple r value is small
D) No, because the standard error value is more than 5
E) Yes, because the standard error value is more than 5

Accepted Answer

The answer of Information was collected from employee records to...

Question 2

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
A) -1
B) +1
C) 0
D) Infinity
E) None of these statements are correct

Accepted Answer

When all the plots on a scatter diagram lie on a straight line, the standard error of estimate is 0 because there is no deviation of the data points from the line, indicating perfect prediction.

Question 3

i. The basic question in testing the significance of rho is to see if there is zero correlation in the population from which the sample was selected.
Ii) A t test is used to test the significance of the coefficient of correlation.
Iii) Suppose a sample of 15 homes recently sold in your area is obtained. The correlation between the area of the home, in square feet, and the selling price is 0.40. We want to test the hypothesis that the correlation in the population is zero versus the alternate that it is greater than zero. You determine that the rejection region should fall in the lower tail if this is a one-tailed test and we use a 0.01 significance level.
A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

Statement (i) and (ii) are correct. Statement (iii) is incorrect because for a positive correlation, the rejection region should be in the upper tail, not the lower tail.

Question 4

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected:   
What is the value of the standard error of estimate?
A) 9.3104
B) 8.778
C) 8.328
D) 86.68
E) None of the choices are correct

Accepted Answer

The answer of A sales manager for an advertising agency...

Question 5

Which value of r indicates a stronger correlation than 0.40?
A) -0.30
B) -0.50
C) +0.38
D) 0
E) None of these statements are correct

Accepted Answer

A correlation of -0.50 indicates a stronger correlation than 0.40 because the absolute value of -0.50 (which is 0.50) is greater than 0.40. Correlation strength is determined by the absolute value, regardless of the sign.

Question 6

If the decision in the hypothesis test of the population correlation coefficient is to reject the null hypothesis, what can we conclude about the correlation in the population?
A) It is zero
B) It could be zero
C) It is not zero
D) It equals the computed sample correlation
E) None of these statements are correct is correct

Accepted Answer

Rejecting the null hypothesis in a test for the population correlation coefficient implies that there is sufficient evidence to conclude that the population correlation is not zero.

Question 7

In correlation analysis, the dependent variable is
A) The variable that is scaled on the horizontal axes.
B) The variable that is being predicted or estimated.
C) A variable that provides the basis for estimation. It is the predictor variable.
D) None of the above.

Accepted Answer

In correlation analysis, the dependent variable is the one being predicted or estimated, while the independent variable is the predictor.

Question 8

Given the following five points: (-2,0), (-1,0), (0,1), (1,1), and (2,3). If the regression equation is Y' = 2 - 0.4X, what is the value of Y' when X = -3?
A) 0.8
B) 3.2
C) -10.0
D) 14.0
E) None of the choices are correct

Accepted Answer

To find Y' when X = -3, substitute X = -3 into the regression equation Y' = 2 - 0.4X. This gives Y' = 2 - 0.4(-3) = 2 + 1.2 = 3.2.

Question 9

i. The basic question in testing the significance of rho is to see if there is zero correlation in the population from which the sample was selected.
Ii) A t test is used to test the significance of the coefficient of correlation.
Iii) When testing the strength of the relationship between two variables, the alternate hypothesis is: H0: ? ? 0.T4
A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements, but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) All statements are false

Accepted Answer

(i) and (ii) are correct statements because they accurately describe the purpose and method of testing the significance of rho. (iii) is incorrect because the alternate hypothesis for testing the strength of the relationship between two variables is H1: ? ? 0, not H0: ? ? 0.

Question 10

In correlation analysis, the independent variable is
A) The variable that is scaled on the vertical axes.
B) The variable that is being predicted or estimated.
C) A variable that provides the basis for estimation. It is the predictor variable.
D) None of the above.

Accepted Answer

In correlation analysis, the independent variable is the predictor variable that provides the basis for estimation.

Question 11

Which value of r indicates a stronger correlation than 0.55?
A) -0.30
B) -0.50
C) 0.30
D) All of the statements are correct
E) None of these statements are correct

Accepted Answer

The answer of Which value of r indicates a stronger...

Question 12

What is the range of values for the coefficient of determination?
A) -1 to +1 inclusive
B) -100% to +100% inclusive
C) -100% to 0% inclusive
D) 0% to 100% inclusive
E) None of these statements are correct

Accepted Answer

The coefficient of determination, often represented as R², ranges from 0% to 100%, indicating how well data fits a statistical model.

Question 13

Which value of r indicates a stronger correlation than 0.25?
A) -0.30
B) -0.50
C) 0.30
D) All of these statements are correct
E) None of these statements are correct

Accepted Answer

The absolute value of r indicates the strength of the correlation. The larger the absolute value of r, the stronger the correlation. Therefore, -0.30, -0.50, and 0.30 are all stronger correlations than 0.25.

Question 14

The correlation between two variables is -0.63 for a sample of 20 observations. Which of the following is a correct conclusion based on the data given? Use the .05 significance level.
A) Reject H0. There is a negative association between the variables.
B) Do not reject H0. There is a negative association between the variables.
C) Reject H0. There is a positive association between the variables.
D) None of the above.

Accepted Answer

The correlation coefficient of -0.63 indicates a moderate negative association. With 20 observations, the critical value for significance at the 0.05 level is approximately ±0.444. Since -0.63 is less than -0.444, we reject the null hypothesis (H0) of no correlation, concluding there is a significant negative association.

Question 15

What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be?
A) Regression equation
B) Slope of the line
C) Standard error of estimate
D) Least squares principle
E) None of these statements are correct

Accepted Answer

The standard error of estimate measures the accuracy of predictions made with a regression line, indicating how much observed values deviate from predicted values.

Question 16

Which value of r indicates a stronger correlation than -0.40?
A) -0.30
B) -0.50
C) 0
D) 0.30
E) None of these statements are correct

Accepted Answer

A correlation of -0.50 indicates a stronger negative correlation than -0.40 because the absolute value of -0.50 is greater than that of -0.40.

Question 17

Which of the following is true about the standard error of estimate?
A) Measure of the accuracy of the prediction
B) Based on squared vertical deviations between Y and Y'
C) Cannot be negative
D) All of these statements are correct
E) None of these statements are correct

Accepted Answer

The standard error of estimate measures the accuracy of predictions, is based on squared deviations, and cannot be negative, making all statements correct.

Question 18

The correlation between two variables is -0.63 for a sample of 20 observations. What is the computed value of the test statistic?
A) 3.442
B) -0.63
C) -3.442
D) None of the above

Accepted Answer

The answer of The correlation between two variables is -0.63...

Question 19

Use the scatter diagrams to verify which statements are correct:
 
Chart A

Chart B

Chart C 
A) The variables in Chart A have a positive correlation
B) The variables in Chart B have a positive correlation
C) The variables in Chart B have a negative correlation
D) The variables in Chart A have a stronger correlation than the variables in Chart B
E) B & D are correct

Accepted Answer

The answer of Use the scatter diagrams to verify which...

Question 20

The partial megastat output below is regression analysis of the relationship between annual payroll and number of wins in a season for 28 teams in professional sports. The purpose of the analysis
Is to predict the number of wins when given an annual payroll in $millions. Although technically not a sample, the baseball data below will be treated as a convenience sample of all major league professional sports.  Refer to the printout above. How many independent variables?
A) 1
B) 2
C) 26
D) 27
E) 28

Accepted Answer

The answer of The partial megastat output below is regression...

Quiz 12: Linear Regression and Correlation

Information was collected from employee records to determine whether there is an association between an employee's age and the number or workdays they miss. Partial excel results are summarized below: Given this information alone, would you decide to continue with the regression analysis?

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this believe, the following data was collected: What is the value of the standard error of estimate?

Which value of r indicates a stronger correlation than 0.40?

If the decision in the hypothesis test of the population correlation coefficient is to reject the null hypothesis, what can we conclude about the correlation in the population?

In correlation analysis, the dependent variable is

Given the following five points: (-2,0) , (-1,0) , (0,1) , (1,1) , and (2,3) . If the regression equation is Y' = 2 - 0.4X, what is the value of Y' when X = -3?

In correlation analysis, the independent variable is

Which value of r indicates a stronger correlation than 0.55?

What is the range of values for the coefficient of determination?

Which value of r indicates a stronger correlation than 0.25?

The correlation between two variables is -0.63 for a sample of 20 observations. Which of the following is a correct conclusion based on the data given? Use the .05 significance level.

What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be?

Which value of r indicates a stronger correlation than -0.40?

Which of the following is true about the standard error of estimate?

The correlation between two variables is -0.63 for a sample of 20 observations. What is the computed value of the test statistic?

Use the scatter diagrams to verify which statements are correct: Chart A Chart B Chart C